The general potential V(x, t) in which Airy wave packets remain nonspreading

We show that for Hamiltonian of the form, H = c(t)partial derivative(x)partial derivative(x) + V (x, t), the general potential V (x, t) for which Airy packets remain nonspreading under time evolution can only be of the form V (x, t)= p(t) x + q(t), where p(t) and q(t) are real functions. We derive rules for constructing nonspreading Airy packets from this general potential. We also consider normalizable packets obtained from Airy packet times a converging factor, such as e e(beta x), with beta > 0. We show that there is no potential which sustains nonspreading wave packets of this kind. Copyright (C) EPLA, 2008.